Surface Pressure and Buoyancy

[drewsteriam]

Ok here goes,
A cubical box 25.00 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.4 kPa and the pressure on the bottom surface is 112.0 kPa. What is the density of the fluid.

I know density=mass/volume and I know my teacher gave us another long formula in class that I never understood so that is about all I know about these problems.

My attempt at a solution: I don't even know what the problem is asking so I don't have much of an attempt at it. If anyone could explain the concept to me and/or let me know of some formulas that might help me that would be great. Thanks

 

[Astronuc]

What is the density of the fluid.

The change in pressure is simply $\rho$gh, where $\rho$ is the fluid density and h is the differential height over which the pressure difference is measured.

http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html

So knowing the pressure at bottom is 109.4 kPa and at top the pressure is 112.0 kPa, equate the difference to $\rho$gh.

 

[ogb p]

Hi there, let me try to break down the problem for you. The problem is asking for the density of the fluid in which the box is immersed. Density is a measure of how much mass is packed into a certain volume. In this case, the volume is the volume of the box, which is given as 25.00 cm on each side (or 25.00 cm^3). So, we need to find the mass of the fluid in the box in order to calculate its density.

To do this, we need to understand the concept of surface pressure and buoyancy. Surface pressure is the force exerted by a fluid on a surface, and it is directly related to the density of the fluid. The higher the density, the higher the surface pressure. Buoyancy, on the other hand, is the upward force exerted by a fluid on an object immersed in it. This force is equal to the weight of the fluid that the object displaces.

In this problem, the box is immersed in the fluid, so it experiences both surface pressure and buoyancy forces. The pressure at the top surface of the box is 109.4 kPa, meaning that the fluid is exerting a force of 109.4 kPa on the top surface of the box. Similarly, the pressure on the bottom surface is 112.0 kPa, meaning that the fluid is exerting a force of 112.0 kPa on the bottom surface of the box.

Now, since the box is completely submerged in the fluid, the buoyancy force on the box is equal to the weight of the fluid that the box displaces. We can use the formula for pressure (P = F/A) to calculate the weight of the fluid. The area in this case would be the bottom surface of the box, which is 25.00 cm^2. So, we can set up an equation:

112.0 kPa = (weight of fluid)/25.00 cm^2

Solving for the weight of the fluid, we get 2800 N. Now, since we know that density = mass/volume, we can rearrange this equation to find the mass of the fluid:

Mass of fluid = density x volume

We know the volume of the fluid (25.00 cm^3), so now we just need to find the density. We can use the formula for density (density = mass/volume) and plug in the